Understand that Family 3 pack means you can have the Product Key used on any 3 machines at the same time, not three times. As with all retail Windows except OEM, you can move it whenever you want as long as it only remains on 3 separate machines.
But if Windows 7 came preinstalled on the machine in question there is no reason to waste a retail license on it since you own that version of the OS on that machine for it's life - to reinstall any way you please.
The disks are all the same with some versions hidden. As long as it is the same version and has SP1 you can use it with the Product Key on the COA sticker, following these steps (which also include the latest official installer) to Clean Reinstall - Factory OEM Windows 7.